Family average by subgroup weights: The average age of all members of a family is 25 years. The average of males is 30 years and the average of females is 20 years. If there are 15 females, how many males are there?
Aptitude
Average
Difficulty: Easy
Choose an option
Answer
Correct Answer: 15
Explanation
Introduction / Context:Another weighted average problem using two subgroup means to deduce the unknown count.
Given Data / Assumptions:
- Overall average = 25
- Male average = 30; Female average = 20
- Females = 15; let males = m
Concept / Approach:Use (30m + 20 * 15) / (m + 15) = 25 and solve for m.
Step-by-Step Solution:(30m + 300) / (m + 15) = 2530m + 300 = 25m + 3755m = 75 → m = 15
Verification / Alternative check:Totals: males 30 * 15 = 450; females 20 * 15 = 300; combined 750 over 30 persons gives 25 average.
Why Other Options Are Wrong:Other values do not satisfy the overall average constraint.
Common Pitfalls:Placing the wrong subgroup count in the numerator or forgetting to add both groups in the denominator.
Final Answer:15